|Table of Contents|

Citation:
 Reza Ghasemi,Farideh Shahbazi,Mahmood Mahmoodi.Fractional Super-Twisting/Terminal Sliding Mode Protocol for Nonlinear Dynamical Model: Applications on Hovercraft/Chaotic Systems[J].Journal of Marine Science and Application,2023,(3):556-564.[doi:10.1007/s11804-023-00329-7]
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Fractional Super-Twisting/Terminal Sliding Mode Protocol for Nonlinear Dynamical Model: Applications on Hovercraft/Chaotic Systems

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Title:
Fractional Super-Twisting/Terminal Sliding Mode Protocol for Nonlinear Dynamical Model: Applications on Hovercraft/Chaotic Systems
Author(s):
Reza Ghasemi1 Farideh Shahbazi2 Mahmood Mahmoodi2
Affilations:
Author(s):
Reza Ghasemi1 Farideh Shahbazi2 Mahmood Mahmoodi2
1. Department of Engineering, University of Qom, Qom 3716146611, Iran;
2. Department of Mathematics, University of Qom, Qom 3716146611, Iran
Keywords:
Fractional-order systemSuper-twisting algorithmTerminal methodologySliding mode controlStabilityNonlinear systemHovercraft
分类号:
-
DOI:
10.1007/s11804-023-00329-7
Abstract:
Fractional terminal and super-twisting as two types of fractional sliding mode controller are addressed in the present paper. The proposed methodologies are planned for both the nonlinear fractional-order chaotic systems and the nonlinear factional model of Hovercraft. The suggested procedure guarantees the asymptotic stability of fractional-order chaotic systems based on Lyapunov stability theorem, by presenting a set of fractional-order laws. Compared to the previous studies that concentrate on sliding mode controllers with unwanted chattering phenomena, the proposed methodologies deal with chattering reduction of terminal sliding mode controller/super twisting to converge to desired value in finite time, consequently. The main advantages of the offered controllers are 1) closed-loop system stability, 2) robustness against external disturbances and uncertainties, 3) finite time zero-convergence of the output tracking error, and 4) chattering phenomena reduction. Finally, the simulation results show the performance of the approaches both on the chaotic and Hovercraft models.

References:

[1] Aghababa MP (2013) Design of a chatter-free terminal sliding mode controller for nonlinear fractional-order dynamical systems. International Journal of Control 86(10): 1744–1756. https://doi.org/10.1080/00207179.2013.796068
[2] Alipour M, Malekzadeh M, Ariaei A (2022) Practical fractional-order nonsingular terminal sliding mode control of spacecraft. ISA Transactions 128(4): 162–173. https://doi.org/10.1016/j.isatra.2021.10.022
[3] Aslam MS, Raja MAZ (2015) A new adaptive strategy to improve online secondary path modeling in active noise control systems using fractional. Signal Processing Approach 107: 433–443. https://doi.org/10.1016/j.sigpro.2014.04.012.
[4] Cabecinhas D, Batista P, Oliveira P, Silvestre C (2017) Hovercraft control with dynamic parameters identification. IEEE Transactions on Control Systems Technology 26(3): 785–796. https://doi.org/10.1109/TCST.2017.2692733
[5] Couceiro MS, Ferreira NF, Machado JT (2010) Application of fractional algorithms in the control of a robotic bird. Communications in Nonlinear Science and Numerical Simulation 15(4): 1–11. https://doi.org/10.1016/j.cnsns.2009.05.020
[6] Djeghali N, Bettaye M, Djennoune S (2021) Sliding mode active disturbance rejection control for uncertain nonlinear fractional-order systems. European Journal of Control 57(1): 54–67. https://doi.org/10.1016/j.ejcon.2020.03.008
[7] Hu R, Deng H, Zhang Y (2020) Novel dynamic-sliding-mode-manifold-based continuous fractional-order nonsingular terminal sliding mode control for a class of second-order nonlinear systems. IEEE Access 8: 20–29. https://doi.org/10.1109/ACCESS.2020.2968558
[8] Jeong S, Chwa D (2017) Coupled multiple sliding-mode control for robust trajectory tracking of hovercraft with external disturbances. IEEE Trans Ind Electron 65(5): 4103–4113. https://doi.org/10.1109/TIE.2017.2774772
[9] Karami H, Ghasemi R (2020) Fixed time terminal sliding mode trajectory tracking design for a class of nonlinear dynamical model of air cushion vehicle. SN Applied Sciences 2: 98. https://doi.org/10.1007/s42452-019-1866-5
[10] Levantovsky LV, Levant A (1987) High order sliding modes and their application for controlling uncertain processes. Moscow: Institute for System Studies of the USSR Academy of Science 18: 381–384
[11] Li R, Zhang X (2022) Adaptive sliding mode observer design for a class of T–S fuzzy descriptor fractional order systems. IEEE Transactions on Fuzzy Systems 28(9): 1951–1960. https://doi.org/10.1109/TFUZZ.2019.2928511
[12] Li Y, Chen YQ, Podlubny I (2009) Mittag-Leffler stability of fractional-order non-linear dynamic systems. Automatica 45(8): 1965–1969. https://doi.org/10.1016/j.automatica.2009.04.003
[13] Lorenz EN (1963) Deterministic non-periodic flow. Journal of the Atmospheric Sciences 20: 130–141. https://doi.org/10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
[14] Magin RL (2006) Fractional calculus in bioengineering. Begell House Redding
[15] Modiri A, Mobayen S (2020) Adaptive terminal sliding mode control scheme for synchronization of fractional-order uncertain chaotic systems. ISA Transactions 105(1): 33–50. https://doi.org/10.1016/j.isatra.2020.05.039
[16] Munoz E, Gaviria C, Vivas A (2007) Terminal sliding mode control for a SCARAR robot. International Conference on Control, Instrumentation and Mechatronics Engineering, Johor Bahru, Johor, Malaysia
[17] Ott E, Grebogi C, Yorke J (1990) Controlling chaos. Physical Review Letter 64(11): 1196–1199. https://doi.org/10.1103/PhysRevLett.64.1196
[18] Petras I (2010) Fractional-order nonlinear systems-modeling, analysis, and simulation. Spring-Verlag, Berlin
[19] Podlubny I (1998) Fractional differential equations: An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Academic Press, 198
[20] Rabah K, Ladaci S, Lashab M (2017) A novel fractional sliding mode control configuration for synchronizing disturbed fractional-order chaotic systems. Pramana - J Phys 89(46): 1443–1447. https://doi.org/10.1007/s12043-017-1443-7
[21] Rook S, Ghasemi R (2018) Fuzzy fractional sliding mode observer design for a class of nonlinear dynamics of the cancer disease. International Journal of Automation and Control 12(1): 62–77. https://doi.org/10.1504/IJAAC.2018.10005623
[22] Shahbazi F, Ghasemi R, Mahmoodi M (2021) Fractional nonsingular terminal sliding mode controller design for the special class of nonlinear fractional-order chaotic systems. International Journal of Smart Electrical Engineering 11(2): 83–88. https://doi.org/10.30495/ijsee.2022.1945459.1160
[23] Sharafian A, Ghasemi R (2019) A novel terminal sliding mode observer with RBF neural network for a class of nonlinear systems. International Journal of Systems, Control and Communications 9(4): 369–385. https://doi.org/10.1504/IJSCC.2018.10012813
[24] Sharafian A, Ghasemi R (2019) Fractional neural observer design for a class of nonlinear fractional chaotic systems. Neural Computing and Applications 31(4): 1201–1213. https://doi.org/10.1007/s00521-017-3153-y
[25] Sira-Ramírez H (2002) Dynamic second-order sliding mode control of the hovercraft vessel. IEEE Transactions on Control Systems Technology 10(6): 860–865. https://doi.org/10.1109/TCST.2002.804134.
[26] Song S, Zhang B, Xia J, Zhang Z (2018) Adaptive back stepping hybrid fuzzy sliding mode control for uncertain fractional-order nonlinear systems based on finite-time scheme. IEEE Transactions on Systems, Man, and Cybernetics: Systems 20(4): 1559–1569. https://doi.org/10.1109/TSMC.2018.2877042
[27] Tavazoei MS, Haeri M, Jafari S, Bolouki S, Siami M (2008) Some applications of fractional calculus in suppression of chaotic oscillations. IEEE Transactions on Industrial Electronics 55(11): 4094–4101. https://doi.org/10.1109/TIE.2008.925774
[28] Utkin V (1992) Sliding mode in control and optimization. Springer Verlag, Berlin
[29] Wang N, Gao Y, Zhang X (2021) Data-driven performance-prescribed reinforcement learning control of an unmanned surface vehicle. IEEE Transactions on Neural Networks and Learning Systems 32(12): 5456–5467. https://doi.org/10.1109/TNNLS.2021.3056444
[30] Wang N, Su SF (2019) Finite-time unknown observer-based interactive trajectory tracking control of asymmetric under actuated surface vehicles. IEEE Transactions on Control Systems Technology 29(2): 794–803. https://doi.org/10.1109/TCST.2019.2955657
[31] Xu H, Fossen TI, Guedes Soares C (2020) Uniformly semiglobally exponential stability of vector field guidance law and autopilot for path-following. European Journal of Control 53(1): 88–97. https://doi.org/10.1016/j.ejcon.2019.09.007
[32] Xu H, Oliveira P, Guedes Soares C (2021) L1 adaptive back stepping control for path-following of under actuated marine surface ships. European Journal of Control 58(1): 357–372. https://doi.org/10.1016/j.ejcon.2020.08.003

Memo

Memo:
Received date:2022-5-20;Accepted date:2022-11-22。
Corresponding author:Reza Ghasemi,E-mail:r.ghasemi@qom.ac.ir
Last Update: 2023-10-10